It "abruptly dies" as in... sounds like you hit the stop switch all of a sudden? That's is an ignition issue. The 128LD/CD is notorious for such issues.
I would start by replacing the spark plug with a brand new OEM part (NOT a knockoff or "substitute" part.) Usual practice is to check the system with an inline spark tester before replacing anything, but I've found that on this model attaching such a spark tester usually causes the problem to suddenly disappear.
If a new, genuine spark plug does not correct the issue, try unplugging the stop switch. There's a plug on the underside of the trimmer with two wires (blue wires, I believe) that goes to the stop switch. With the stop switch unplugged, you can use the choke to stop the trimmer. I've had a few of those with intermittent ignition issues due to the stop switch failing.
If neither the stop switch or spark plug is causing an issue, it's the ignition coil (or coil wire, but they're both one piece.) If the ignition coil requires replacement, you may want to take it to a shop if your mechanical skills are limited. It's a rather involved repair and requires removing the engine from the trimmer.
On a side note, is the new carburetor a genuine Husqvarna part, or an aftermarket knockoff?